This article is about the derivative of a product. For the relation between derivatives of 3 dependent variables, see Triple product rule. For a counting principle in combinatorics, see Rule of product. For conditional probabilities, see Chain rule (probability).
Geometric illustration of a proof of the product rule
In calculus, the product rule (or Leibniz rule[1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as
or in Leibniz's notation as
The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts.
In calculus, the productrule (or Leibniz rule or Leibniz productrule) is a formula used to find the derivatives of products of two or more functions...
The triple productrule, known variously as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, is a formula which relates partial...
In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated...
non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral...
the antiderivative of a product of functions into an antiderivative for which a solution can be more easily found. The rule can be thought of as an integral...
the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the productrule (which is also known as "Leibniz's rule"). It states that...
differentiation – Calculus property Productrule – Formula for the derivative of a product Reciprocal rule – differentiation rulePages displaying wikidata descriptions...
Leibniz integral rule – Differentiation under the integral sign formula Productrule – Formula for the derivative of a product Quotient rule – Formula for...
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors)...
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation...
\mathbf {B} )\end{aligned}}} We have the following generalizations of the productrule in single-variable calculus. ∇ ( ψ ϕ ) = ϕ ∇ ψ + ψ ∇ ϕ ∇ ( ψ A ) = (...
triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or triple...
slope. In particular, this notation is powerful because the gradient productrule looks very similar to the 1d-derivative case: ∇ ( f g ) = f ∇ g + g ∇...
readily deduce the quotient rule from the reciprocal rule and the productrule. The reciprocal rule states that if f is differentiable at a point x and...
Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian...
functions. For constant rule and sum rule, see Apostol 1967, p. 161, 164, respectively. For the productrule, quotient rule, and chain rule, see Varberg, Purcell...
the productrule and the reciprocal rule. The elementary power rule generalizes considerably. The most general power rule is the functional power rule: for...
portal Chain rule Differentiation of integrals Leibniz rule (generalized productrule) Reynolds transport theorem, a generalization of Leibniz rule Protter...
\mathbf {F} +\varphi (\nabla \cdot \mathbf {F} ).} Another productrule for the cross product of two vector fields F and G in three dimensions involves...
products. In the following, mainly atomic and molecular transitions are considered. In quantum mechanics the basis for a spectroscopic selection rule...
of differentiation Power rule Chain rule Local linearization Productrule Quotient rule Inverse functions and differentiation Implicit differentiation...
one-dimensional quadrature rule, but performs a more sophisticated combination of univariate results. However, whereas the tensor productrule guarantees that the...
Global Information
